[codeismath]

I think numbers are wonderful and cool abstract thingies. We grow up being taught them (in my case Arabic numerals in base 10) and they become such part of our being that we start to think that we know what “5” is. Then I was introduced to Roman Numerals. Didn’t like those much. That one taught me that 4 is more related to 5 than it is 3. Then some of us learn a base 2 number system or base 16 number system and for a brief moment we question whether we actually knew what “5” was. And then we may learn about Peano and the successor(s…) of zero. Did we really know what “5” was then? What is five-ness really? Perhaps fiveness is a set within a set within a set…

Every interaction our human minds have with fiveness is with a representation or encoding of 5. With each new representation, I’ve experienced fiveness slightly differently.

But I like computers and math. For me, the best to experience oneness with the fiveness is through computation with Lambda Calculus and Church Numerals. Very fond of that encoding.

[Koshkin]

> Did we really know what “5” was then? What is five-ness really?

Ah, but we do, and it’s very simple: it is what five cows an five fingers have in common in the most obvious sense. There’s no mystery there.

Or, stated in another way, “fiveness is something you’ll be very sad not to see when you look at your hand.”

[orthonormal]

I lost one of my fingers when i was a child, so after getting used to it i don't experience sadness when i look at it. That statement also checks out for four, in this case.

[lazydud]

Ok

[esarbe]

This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition.

I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system.

So, given that there are no categories to put discrete things into - they just exist in our imagination - and there are probably not even discrete things - these also just exist in our imagination - the question of five-ness is not really answered.

[Radim]

> You cannot separate a river from the ocean - it's part of the same system.

> discrete things - these also just exist in our imagination

What leads you to separate "imagination" from "exists"? Isn't imagination also "part of the same system"?

Imagination definitely has the capacity to affect the world, so it's not obvious in what way it's "not real". Why do you draw a hard line there?

[Koshkin]

More to the point, the idea that "you cannot separate a river from the ocean" seems to be ostensibly wrong - otherwise we wouldn't have the (very useful in practice) notions of 'river' and 'ocean' in the first place. If you look at a map, the differences stand out pretty clearly - e.g., a river has a starkly different topology from that of the ocean. So, no, these differences are not just figments of our imagination, as, in particular, everyday practice shows.

In general, the failure to perceive emergent phenomena as something different from the particular substrate, and consider it separately - for instance, the failure to see how nature is not just a bunch of atoms moving around, has a name - reductionism. It is a form of intellectual blindness (not to be confused with the ability to think abstractly).

[esarbe]

I'm not drawing a hard line at all; yes, imagination is part of the same system. And of course it has the capacity to affect the world.

I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

[Radim]

But "world", "separate" and "parts" are all language concepts too. I feel the inconsistency in your (circular) argument is not getting through.

That divisions are arbitrary and "exist just in our imagination" doesn't line up with your admission that imagination is real, and using words to describe it. That line between "real" vs "arbitrary / imaginary" is not as clear cut as you (unconsciously, apparently) draw it.

[esarbe]

> I feel the inconsistency in your (circular) argument is not getting through.

I guess it's not, since I'm not convinced that mine is a circular argument.

My argument - to put is simply - is that we are all part of the same system and that there are no divisions. Without divisions, no numbers. I don't need any distinction between 'real' and 'arbitrary' for this to hold, that's a dichotomy you assume on your part.

[trashtester]

> I'm just pointing that without arbitrarily dividing the world into separate parts, numbers don't arise.

I agree. Though I think a stronger statement is also true: Without "arbitrarily" dividing the world into separate parts, non-trivial thought is not possible.

Assuming by "parts", you mean "categories", I think my statement is still true. And, once we have categories, we can use numbers to compress information, which in terms allow us to perform more complex computation/though with our limited computational power.

As to how arbitrary our categories are, one could argue that some are hardwired to our DNA, as claimed by Chomsky(1).

[1]: https://en.wikipedia.org/wiki/Universal_grammar

[vageli]

> This presumes the existence of a category like 'cow' or 'finger'. I'm pretty sure there's nothing intrinsic about 'cows' and 'fingers'; these are artifacts of human cognition. I base reality, there are no such things as 'cows' and 'fingers'. Just systems with similar properties. And if you have to be very pedantic, there are not even discrete systems, since everything is linked by information. You cannot separate a river from the ocean - it's part of the same system.

When I cut my finger the cow does not share in my pain. When we kill the cow for its meat, we do not share in its pain. That the cow becomes part of us through its consumption does not seem to invalidate this point—discrete systems do exist in our experience.

Of course, if you zoom out far enough you might refer to the sum of those discrete parts as some singular, complex system, but it seems the human experience is fairly limited in exposing this subtlety (not to mention that it is often useful to discuss the parts themselves without considering their relationship to the entire universe).

[trashtester]

Also, the concepts "artifacts", "human", "human cognition" and "artifacts of human cognition" are all example artifacts of human cognition.

As is "circular", "reasoning" and "circular reasoning", as well as "irony".

[Koshkin]

I don't know about that. Reality is strongly suggestive. (Of course you can argue that "reality" also is a figment of our imagination or, for example, it's not a thing in the first place, but I personally wouldn't go that far.)

[saeranv]

Does the base really have anything to do with 5? I can represent 5 in base 10 as 5, or I can represent it in base 2 as 101, but both encode the same information.

Using different bases, to me, is just about storing information. How many symbols do you want to create before you increase the length of your number and start re-using them.

[routerl]

In fact, you're talking about digits and numerals, not numbers. But this actually drives your point home, I think.

[lisper]

> What is five-ness really?

It is everything that has some relation to something that has that same relation to something that has that same relation to something that has that same relation to something that has that same relation to some unique thing that does NOT have that same relation to anything.

[function_seven]

Is this the spoken form of a Church Numeral or something?

[lisper]

Yes. Exactly. (You could also see it as a rendering of some of the Peano axioms.)

[BBC-vs-neolibs]

Username checks out. :)

[LudwigNagasena]

I would say that positional notation, Zermelo ordinals and Church numerals are just ways to encode numbers. I would never call them numbers in the strictest sense of this word. Just how your C code is not an algorithm.

I would say I knew what 5 was even before I learned any notation or written language whatsoever.

[ayewo]

> Did we really know what “5” was then? What is five-ness really? Perhaps fiveness is a set within a set within a set…

The reason it seems mushy is because there are two related concepts at play: a numeral vs. a number.

A numeral is the symbol: 5 in Arabic numerals in Latin script or ٥ in Arabic script; V in Roman numerals etc.

A number is the quantity, the amount being expressed: five (English), ḫamsa (Arabic), cinq (French) etc.

[stareatgoats]

Yes; the difference between token and denoted concept. They are not the same thing (as René Magritte probably wanted to say with his "This is not a pipe" painting). In computer contexts: each representation of 5, in whatever base or language would point to the same element in a lookup-table.

But for us humans, the tokens and concepts blend to some degree: maybe not so much with regards to numerals (although there seem to be exceptions ...). So even if 'Amour', 'Love' and 'Liebe' essentially point to the same concept, we might conceive of them differently, ever so slightly, depending on the language we chose to use.

Which gives an inkling of the vast difference between computers and humans, at the current stage.

[ornxka]

Five's how many fingers I have.

[trashtester]

Sorry to hear that... May I ask how you lost the other 5?

(My inner Asberger's could not resist.)

[jychang]

Five Five Five Five Five

There is no Antimemetics Division

[nonsen]

5 means territory